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 Post subject: Horizontal Mixing
PostPosted: Wed Feb 26, 2003 4:19 pm 
Dear ROMS users,

I have problems specifying proper values for diffusion and viscosity coefficients (TNU2, VIS2). It seems there is more guess work involved than calculation.

Furthermore, it seems that the advection algorithms have some kind of intrinsic smoothing (at least the default upstream bias), so horizontal mixing values are not really needed. Does anyone have documentation or information on how to calculate these values?

As a beginner, I would appreciate any help.

Regards,

Frank Koesters


Last edited by koesters on Fri Nov 21, 2003 8:38 pm, edited 1 time in total.

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 Post subject: Re: Horizontal Mixing
PostPosted: Wed Feb 26, 2003 4:20 pm 
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Joined: Mon Apr 28, 2003 5:05 pm
Posts: 5
Location: IMCS, Rutgers University
Hi Frank:

Yes, upstream bias advection carries with it some intrinsic smoothing. A typical choice would be upstream advection of T and S, but little or no explicit harmonic or biharmonic smoothing (weak diffusivity).

By "little or no" I mean relative to the usual values one would use. These would be chosen to give a predetermined viscous time-scale for the shortest-scale (2 delta-x) waves.

Typically, you would want to have the explicit viscosity have a 2dx timescale short enough to be important relative to other dynamics. In practice, this would usually mean a timescale shorter than a day. Therefore, you would want to pick a viscosity something like:

visc2 ~ (delta_x / pi)**2 / timescale

visc4 ~ (delta_x / pi)**4 / timescale

for harmonic and biharmonic mixing where timescale is a fraction of a day (a quarter to a half perhaps).

This ensures that viscosity is working on 2_dx features (which are inaccurate in any case) but not too strongly.

You notice that I have used words like "usually" and "typically" quite frequently. That is because choosing these parameters is more artistry than science. Nonetheless, the abovementioned rules of thumb often work OK.

Regards,

dale


Last edited by dale on Fri Nov 21, 2003 8:40 pm, edited 1 time in total.

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 Post subject: RE: Horizontal Mixing
PostPosted: Wed Feb 26, 2003 4:21 pm 
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Joined: Wed Jul 02, 2003 5:29 pm
Posts: 3216
Location: IMS/UAF, USA
There is a bit of trial and error here for the most experienced of us. The North Atlantic DAMEE runs were done with upstream bias advection of velocity and tracer, without explicit horizontal smoothing. If you look for it, you can see residual 2 dx noise, especially in mid-depth vertical velocities. Another variable is how smooth is "smooth enough".

Something in the model is producing numerical 2 dx noise at some unknown rate. The Laplacian smoothing will damp that out on a timescale of

t_damp = (2 dx)^2 / ((2 pi)^2 nu)

or

t_damp = (dx)^2 / (pi^2 nu)

You can work out how long it will take to smooth things at 2 dx from this, also things at larger scales, such as that 8 dx eddy you really want to keep. The corresponding biharmonic formula is:

t_damp = (dx)^4 / (pi^4 nu)

Other decisions are whether to rotate the mixing or not. There is some question about the correctness of the u,v rotation and it is advised not to rotate the viscosity. For diffusion, we like to rotate to z surfaces at least.

Kate Hedström
kate@arsc.edu


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